How do I get my file to export as a .stl?
The Local View is enabled for this object in your file. 

 


  Local view isolates the selected object or objects, so that they are the only ones visible in the viewport.  


manual page

Press NumpadSlash to exit it, select the object and try exporting again.

A side note:
- although you recalculated normals some of them are still inverted (the bottom);
- the topology of the mesh is a bit off, especially on the bottom, which can cause unexpected results when triangulated.
- scale of the mesh isn't applied (which can also be undesired);
However, this doesn't affect your current problem directly.